Fractional Dynamics Fire Hawk Optimization for Smart Multi-Modal Logistics Networks under Stochastic Demand

Subject Areas : International Journal of Smart Electrical Engineering

Hosein Esmaili ¹ , Mohammad Ali Afshar Kazemi ^{2 *} , Reza Radfar ³ , Nazanin Pilevari ⁴

1 - Department of Industrial Management, Science and Research Branch, Islamic Azad University
2 - Department of Industrial Management, Science and Research Branch, Islamic Azad University
3 - Department of Industrial Management, Science and Research Branch, Islamic Azad University, Tehran, Iran
4 - Department of Industrial Management, West Tehran Branch, Islamic Azad University, Tehran, Iran

Received: 2025-01-23 Accepted : 2025-06-05 Published : 2025-07-12

Keywords: Multi-modal logistics optimization, Fractional differential equations, Fire Hawk Optimization Algorithm, Stochastic demand modeling, Dynamic network flow analysis.,

Abstract :

Optimizing dynamic multi-modal logistics networks is vital for efficient resource allocation and cost minimization under stochastic demand. This study develops a robust framework integrating fractional differential equations for modeling temporal flow dynamics and employs the Fire Hawk Optimization Algorithm (FHOA) to address the resulting complex optimization problem. The proposed framework represents logistics networks as directed graphs, incorporating stochastic demand modeled using Gaussian perturbations and fractional derivatives to capture memory effects. Validation using the Barcelona logistics dataset reveals a total cost reduction of 8,835 units, average flow stabilization at 3.05 units, and resilience under demand variance of 52.32. The model effectively identifies critical edges with high flows, balancing throughput and minimizing costs across scenarios. Furthermore, the algorithm enhances decision-making by optimizing transportation policies and resource allocations, ensuring operational efficiency under uncertainty. The study's findings emphasize the significance of integrating advanced mathematical modeling with metaheuristic optimization techniques to tackle the inherent complexities of logistics systems. These insights provide a scalable and adaptive solution for real-world multi-modal logistics networks.

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